Thursday, July 31, 2003

Father William:

Apparently, if you have the C150T mutation in your mitochondrial DNA, you stand a good chance of getting old. Very old.

Seventeen percent of a group of 52 Italians between 99 and 106 have it, while only 3.4% of 117 people under 99 had it. That's statistically significant, but we still don't understand how the mutation appears (is it inherited or is it a mutation that occurred after conception) or how this affects lifespan (does it contribute to accelerated replication?).

Here's the link to the PNAS 100 (3) 1116-1121 Feb 4 2003 abstract.

What I always found intriguing about mitochondria (wow, there's a cocktail conversation stopper...) is that they use a prokaryote coding scheme, and replicate completely independently of the surrounding (eukaryote) cell. What this probably means is that at some distant point in eukaryote ancestry we had a commensal relationship with a prokaryote, which slowly lost its independence and identity.

Flash to a future actuarial table: "...mtDNA/C150T: Yes/No..."

Flash to a future breakfast cereal advert: "...New! Loaded with mito-DNA enhancing minerals!"

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 Wednesday, July 30, 2003

Addio, Galileo:

Since October 18 of 1989, when it was launched on the shuttle Atlantis during STS-34, the Galileo probe has been hard at work in space. After a seven-year voyage to Jupiter, it was to carry out a two year long survey of the planet and its myriad moons. Amazingly, the probe actually endured radiation and collisions with debris, returning scientific data five years past its designed lifespan.

JPL controllers used up the last of the propellant onboard to put Galileo on an orbit that will take it into the atmosphere of Jupiter on September 21, where it will burn up, returning data even as it melts into oblivion.

Just as with the probes to Mars and the amazing Pioneer and Voyager missions, we tend to personify these machines, and feel some sense of loss when they finally fail. It always brings a tear to my eye to think of the probes that automatically searched for signals from Earth after contact was lost -- vainly listening with their little electronic dishes to the wrong part of the sky after we mistakenly over-wrote part of their programming with a mistaken command until their power supplies wore down or a part failed and they got stuck... sniffle.

As the IKEA man would say, in the Cannes-prize-winning advert Spike Jonz produced about a lamp left out in the rain on a garbage pile: "Many of you feel bad for this spacecraft. That is because you are crazy. It has no feelings. And the new one is much better."

Except, of course, Congress has totally mucked up the schedule for the much better new one.

 Tuesday, July 29, 2003

Poindexter, Wolfowitz, Daschle, Dorgan, Wyden & Warner:

Policy Analysis Market (PAM): http://www.policyanalysismarket.org is now a blank page.

Sigh. Here's a great example of what politics and law are all about, and how they often clash with rational thought. As one of my law professors said during the very first class: "Don't expect law to be about logic. It's not. It's about emotions -- and emotions are not logical."

A fellow Caltech alumnus of some renown, Ret. Adm. John Poindexter, now at DARPA, implemented a plan to use futures markets as predictors of terrorism. Regardless of the fact that the idea makes for really great political fodder, and it sounds a little kooky, the idea actually works. It is based on the fact that people tend to make more conservative and therefore probably truthful guesses about outcomes of uncertain situations when they have a stake in them, and therefore accurately mirror the wider public. These market set-ups have been shown to be more accurate than pundits with things like elections and box office returns, as in the University of Iowa's Tippie College of Business Iowa Electronic Markets Program (IEM). The research involved in the ideas behind the IEM project is not trivial, and has the financial backing of the Department of Education, the National Science Foundation, Microsoft, and NASDAQ. Heck, I remember listening to Minnesota Pubic Radio's "Markeplace" and "Future Tense," who had spots on the idea on November 6th 2000, and February 28th 2003 (see archive), and sang its praises.

The terror futures market program at DARPA was being set up with the help of people who are not fools either: NetExchange and The Economist. The study was not really intended to be focused on individual terrorist acts, but on much wider phenomena, at which these types of things excel. The focus was more along the lines of: "How would public opinion in Jordan shift if X or Y happened."

I was amazed to see how few of the news stories that ran about the Pentagon's defense and then withdrawal of the program actually referred to the research showing that this technique works - the focus of the stories was of course more on the political scandal.

If the Senators are shocked, shocked by 'betting parlors' they should be consistent and shut down all futures markets. Especially those dealing in pork bellies, but I imagine there might be an objection from New York's junior Senator. The amazing thing is that no one seems to have picked up on the sheer hypocrisy of the situation at the Pentagon briefing dealing with the cancellation of the DARPA Program. Immediately after dealing with a question about how shutting down the program was the right thing to do, DOD spokesman DiRita took a question about how the NYSE had ticked up 85 points in one hour in response to rumors about the capture of Saddam Hussein. "Hellllooooo!" The NYSE is a futures market in constant operation, only this one is a little more difficult for offended Senators to shut down for political profit.

Luckily, only $600K of the planned $8 million DARPA investment in PAM had been sunk - but the quotes in the news from the legislators made it sound like the $8 million had already been used.

I do have to agree that there were some skewed incentives involved in PAM, and that perhaps more analysis was needed on political implications of this particular application of the technique. Manipulation through deliberate acts of terrorism make this an easier market to control for the perpetrators than controlling the outcome of an election or movie-goers viewing choices. But the fundamental idea behind the market remains sound - if you have money on the line, you tend to make a better guess. Any arguments about the technique itself, well, are just a load of pork bellies.

 Monday, July 28, 2003

Lynch, Jones:

With all the media attention being paid to the PFC Lynch rescue story, I began to wonder about other 'heroes' from history, and the role of the media and technology in the development of heroes.

With so much scrutiny, the initial stories of the rescue from the hospital, the exact circumstances of the initial ambush and the actual injuries sustained began to be blurred. What had been initially seized upon as a real story of heroism took on a bit of a strange color.

My question is, with all of the access we have to dates, facts and figures, as well as the incessant hunger to expose someone to get a better story, is it a lot more difficult today to produce a 'clean' hero? Would, say, John Paul Jones actually have been quoted as saying "We have not yet begun to fight!" or would the Drudge Ink & Quill Report have something like:

...a diminutive and slightly rumpled Jones emerged from his cabin, only to be informed by the trembling cabin-boy that HMS Serapis had already delivered a crippling blow to the Bonhomme Richard, thus disturbing his daily nap. Several sources are said to have overheard him mumble: "...wha... we have not yet begun to fight?..." and this stumble eventually led to his disgrace and later flight to service in the Russian Navy.

Or will we, as Americans now view Jones through the lens of time, see PFC Lynch as a heroine of the second Gulf war? Will time undo all the access to the ugly details of a story that technology has enabled?

Wait and see. But you might have to wait 200 years.

 Friday, July 25, 2003

Lyakhov & Aleksandrov:

Twenty years ago*, aboard the venerable Salyut 7 Soviet space station, cosmonauts Vladimir Lyakhov and Aleksandr Aleksandrov heard a sound no space-farer wants to hear: CRACK!

The cosmonauts started emergency evacuation procedures, fearing that the hull had been pierced and they were losing air. After a few minutes it became clear that the air pressure was not dropping, and they began to explore the station to find the cause, eventually finding a 3.8 cm impact crater in an observation port. Luckily, the impact had not pierced all the layers in the window.

This particular incident was attributed by the Soviets to the Delta Aquarid shower, but there is also the possibility that it was caused by man-made space debris -- something Lyakhov himself later contributed to by casting off junk during his November 1 1983 spacewalk. All subsequent Russian space station modules have had armored covers over their view ports that are supposed to be closed when not in use.

Aleksandrov later went on to work for the Energiya Design Bureau on rescue systems, and in 1989 he compiled some interesting numbers on spaceflight 'anomalies' during the Vostok, Mercury, Voskhod, Gemini, Soyuz, Apollo and Soyuz series:
  • over 30% were due to human failures
  • 21% were control system failures
  • 85% had no impact on the mission
  • 6% required the use of backup systems
  • 2.5% were self-correcting
  • 0.5% had both the primary and secondary backup systems fail


Pity there is no comparison with Shuttle.

There is an amazing amount of debris in space around the Earth. J-Track 3D is the best Java applet illustration I have seen of the sheer number of satellites that orbit the Earth (and for teaching orbital mechanics, for that matter). If you consider the number of tiny particles that each rocket booster generated in placing these items in orbit, you can get a general idea of how much of a man-made hazard we have put into orbit. Tiny, brilliant pebbles indeed.

*There is some disagreement in the literature over whether this happened on July 25 or July 27.

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 Thursday, July 24, 2003

Altitude vs. Latitude mad science:

Asked by Scott, a video producer from Brooklyn, NY:

I am trying to determine a rough correlate between altitude and latitude, to determine 'apparent latitude' of several ancient mountain observatories in China. Specifically in reference to mountain top star viewing of horizon events along the ecliptic (helical rising and setting of stars). For example: at Latitude 50 N. Pleiades set near the ecliptic about 15 minutes after the sun on the equinox of 2400 BC. At Lat. 35 N. [the Yellow River valley] how high up a mountain would one have to be in order to observe this event at Lat. 35 N. - if possible at all? The point of interest is in dating the received lore of certain events related to the creation of the Chinese calendar. Otherwise that 'conjunction' of the sun and the Pleiades would not be seen at lat. 35 N. until about 2000 BC (dates approximate for purposes of question). Looked at the other way: would say 10,000 feet of altitude provide a view of celestial events on the horizon otherwise only seen from the ground at Lat. 50 N.? To put it succinctly: How high up does one need to be to extend one's 'apparent' view of the east and western horizon to 'events' 5, 10, 15 degrees north?

This was a very interesting set of questions, and I spent too long trying to get a really thorough list of things to think about for you -- I apologize for the delay in answering.

It's fairly easy to get a formula for a spherical Earth with no atmosphere, but there are several tricky things to think about for a really accurate answer. I'll get to those later.

Let's start with the simplest part - a spherical Earth with no atmosphere.
The figure below (labeled 2-2 because I took it from a Celestial Navigation site?) shows an observer standing on the surface at altitude HE (which could be his height above the sea). The angle which the observer has to look down to see the Horizon is called the Dip angle by surveyors and celestial navigators.



Note that the observer's line of sight touches the surface (the Visible Horizon) at a tangent point. Since the Earth is assumed to be spherical, this line is perpendicular to a line from the center of the Earth to the tangent point. Some high school geometry, trigonometry, and algebra should convince you of the following:

1. The triangle is a right-angled triangle.
2. The angle at the center of the Earth is congruent to the Dip angle.
3. The dip angle can be determined from the following formula: Dip = arccos (R/(R+HE))
4. Inverting this for HE in terms of Dip gives: HE = R (sec (Dip) - 1)

Now, here's a bit of a twist. Imagine you are standing at altitude HE at some latitude lambda, but looking directly North. Your dip angle is described as above. Notice that your line of sight still touches the Earth at the Visible Horizon, or tangent point. Therefore, this line is equivalent to your geoidal horizon if you were standing at sea level at that higher latitude! In other words, at altitude HE, you can see farther North by lambda + dip, and will be able to see circumpolar stars with lower declinations.

OK, so how big is this effect? Well, it's pretty small. In fact, taking your examples of how high would you have to be to see 5, 10 and 15 degrees farther North, using a radius for a spherical Earth of 6371 km, you can use equation 4 to find out that you have to be VERY high (24, 98, and 225 km respectively). In other words, you would have to be in an U-2 or spaceship to see that far around! An altitude of 10,000 feet (3048 m) would give you a Dip of only 1.77 degrees.

When you look East or West, this simply changes the rise/set times by a matter of minutes.

You should also be aware of how sensitive these formulas are to errors in measured height. Try a few different heights, and you will see that arccos in this range is not very useful?

As we'll see, the dip angle is similar in size to some of the other complications.

A big effect comes from Atmospheric Refraction, which bends the path of the light from the stars as they pass through the atmosphere. This effect depends on the density of the air, so it is affected by the temperature of the various layers the light passes through. In general, the air gets less dense as you increase in altitude, so light will in general tend to curve towards the Earth's surface as it enters the atmosphere. Notice that this means you can actually see things that are below the Sensible Horizon of Fig. 2-2!

There are two important thing to note about refraction: first, it does not affect things directly overhead, but increases its effect as the viewed object approaches the horizon, and second, it depends on the state of the atmosphere between you and what you are observing. This means that your altitude will affect the size of the refraction, as will weather, atmospheric inversions, etc. etc. Pretty much a mess, if you are trying to be super accurate. How big is this effect? Well, at the worst it is about 35 seconds of arc, so that means that standing at sea level you actually see slightly over 180 degrees of sky! Note that the effect of refraction decreases with Height above Mean Sea Level and with the altitude (angle from vertical) of the observed object.

The next effect to think about is Geocentric Parallax which is related to the fact that the origin of your spherical coordinate system is the center of the Earth, but you are actually observing from several thousand kilometers away from that point, on the surface. Now, if you are observing the Moon, this effect is important since the distance between the centers of the Moon and the Earth is not too much larger than the radius of the Earth. However, when observing stars, the distance to the star is so much greater than the radius of the Earth that this effect is negligible and we can ignore it. For more info on this issue, see http://star-www.st-and.ac.uk/~fv/webnotes/chapt13.htm

The next thing to take into account is the Oblateness of the Earth, which refers to the fact that the Earth is not quite a sphere, but is shaped, to first order, like a slightly flattened ball. This means that for a given latitude, you will be able to see a little farther toward the nearest Pole and a little less towards the Equator than on a sphere. On Earth this effect is small because the oblateness is small, at its maximum at 45 latitude, about 12 seconds of arc, so it can be ignored here.

A much greater effect will be caused by Precession of the Equinoxes which is the change in the location of the celestial poles of rotation. Since you are dealing with dates up to 6,400 years in the past, this is about a quarter of the precessional cycle of 25,800 years, the stars were rotating about a point very different from today, somewhere in the constellation Draco. This changes the whole coordinate system for the stars, and is the largest factor by far -- make absolutely sure you are correcting for this.

The last complication that I can think of is the calendar system that you are relying on - as with the West, I am sure that the Chinese calendar was altered as observations and as political issues came and went. Since at some point you must make a transformation from a Chinese calendar to an astronomical one, this will be important.

I hope this gave you a good list of things to think about as you approach this problem. For more detail and some diagrams on many of these effects, I recommend this Celestial Navigation site.

 Wednesday, July 23, 2003

Eclipse mad science:

Asked by Ernest, a teacher in California: Would it be possible to create an artificial solar eclipse using a circular object in earth orbit to cast a shadow on our planet's surface? If such an orbiting object were at a distance of the international space station, how big would it have to be? Could an artificial eclipse be used as a weapon by denying sunlight to a certain city or country? What might it's potential be as a tourist attraction?

It would certainly be possible to create an artificial eclipse by orbiting a circular object around the Earth, but it wouldn't be very practical.

If the object were orbiting at the height of the International Space Station, or about 380 kilometers high, then we can figure out how large it would have to be to just cover the face of the Sun. The Sun is, on the average, 149,600,000 km from the Earth, and its diameter is 1,392,000 km. Using some trigonometry, that means that it subtends an angle s of about s=2*arcsin(1,392,000/2/149,600,000) or about 0.533 degrees. It's hard to believe the Sun is that small in the sky, isn't it? [Of course, the Moon is also approximately this size, otherwise we'd never see a total solar eclipse!]

Now the object we are thinking about has to subtend the same angle, so again we can use trig to find that if it is 380 km away, it will have a diameter d of about d=2*380*sin(s/2)or about 3.5 km.

Building something this big in orbit is pretty difficult, but possible---the best thing would probably be to simply fire an enormous balloon into orbit and then inflate it until it reached this size. Still, a pretty great feat.

However, notice two things about our scheme: one, the shadow only just touches the ground, and two, the shadow is moving along the ground at least at 17,000 km/hr as the object orbits the Earth (at the same speed as the International Space Station, since it is at the same height). So, unless the shadow were a lot larger (by making the balloon larger), the eclipse would not last long at all. Even the Moon can only cover the Sun for about 4 minutes. The physics of orbits make it impossible to keep the shadow still.

"Aha," you say, "...but what about geostationary and Lagrange orbits?" Well, these orbits are much farther away, and that means that our object needs to get proportionately larger. A geostationary orbit, which is one that orbits the Earth once a day (and so keeps up with the ground underneath it, and therefore seems to stay still in the sky), is 35,767 km from the Earth---our object would have to be 329 km across! The Sun-Earth Lagrange point, where the gravitational pulls of the two bodies are equal, is at about 1,500,000 km, so our object would now have to be 13,816 km across! But note that even for both of these ideas, the shadow would still not stay over the same point on the Earth.

There is actually a satellite called SOHO that is orbiting around the LI Lagrange point 1,5000,000 km sunward from the Earth, and it uses a special camera with a disc in the middle to create its own "artifical eclipses." This is used so that SOHO can observe the solar corona all the time to study the Sun and give us warnings when there are particularly dangerous flares.

The above calculations give us the answer to your question about denying people sunlight, and about creating a tourist attraction where the Sun was always in eclipse---it is pretty much impossible to do it from orbit. The only way to tackle this from orbit would be to build a ring around the Earth (like a ping pong ball with the ends cut off). I will leave it to you to calculate what the surface area of a shell like this would be, but even for a really narrow one, it would take an enormous amount of material.

The opposite idea, that of putting more light on the surface, has actually been tried. Reflecting light off large orbiting mirrors has been proposed to help increase solar arrays generate power or simply to illuminate areas during winter. The Soviets and Russians seriously investigated trying to shine sunlight on Siberia during their long winter months, but gave up after they calculated the size of mirrors and the cost of systems to keep them properly pointed. The idea was also probably strongly opposed by their own astronomers, who need dark skies for observing---read this ABC article about the project.

From Energiya's Znamya site:


Illumination from space - "Tretie svetilo" (Third light):

Solar light from space: This program was also developed during the Columbus-500 project. Illumination by space mirrors was originally proposed by scholars of the past: F. Tzander, H. Obert. Conceptually however, it was developed and refined by Kraft Ericke. Using the solarcraft as a basic component, a whole system can be configured.

The following parameters are considered to be suitable in the near future.


  • Size of reflector---200 m,
  • circular orbits of 1500--4500 km of attitude,
  • size of light spot---15--45 km,
  • brightness 10--100 lunettes (full moon),
  • number of reflectors in a cluster ~ 12,
  • one cluster could provide illumination to 5 large cities.



Here are some stories on the June 21 eclipse, visible in Southern Africa, "Africa Marvels at First Eclipse of New Millennium" and "Africa Marvels at Solar Eclipse," and here's a description of eclipses in general. [You might also check out The Eclipse Home Page.]

Hope this helps!

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 Monday, July 14, 2003

Boat wakes mad science:

Asked by Lonnie, a science grad student at Virginia Commonwealth University: When flying I often see the trails of where boats have passed. These are obviously not wakes. They generally appear as a lighter colored path showing where the boat travelled. What causes this anomaly in the water's surface appearance?

They actually are wakes. I know exactly what you mean, because I have wondered about them too ? they aren?t the wave trains we?re used to that water skiers jump over, but much longer features trailing many kilometers behind.

Here are some images of ship wakes taken from the Space Shuttle, which include examples of what you are interested in.

It turns out that wakes are pretty complicated things. In fact, this particular type of feature is not yet fully understood, because most dynamical solutions damp out to a level that should be unobservable this far downstream from the ship. What you are seeing is probably a non-linear interaction between some of the wake features I talk about below.

Being able to see these features requires a special combination of circumstances. First, the state of the sea itself has to be calm enough so that this feature is not swamped out. Second, the lighting angle has to be right. Notice in all the photos in the NASA link above that nearly all the wake features are most visible near the point of maximum reflection of the sun ? since the sea provides a specular surface, the reflection of the sun is ?smeared out? over a wide area, providing brilliant illumination that allows you to see very fine details and differences in the sea state (things like eddies, wakes, squalls, etc.). Third, the ship has to be going the right speed, and passing over the right kind of water for non-linear effects to appear.

A ship?s wake is composed of many different phenomena:

1. The familiar set of spreading waves in a 19.5 degree angle V behind any ship is called the ?Kelvin wake? after Lord Kelvin, who gave the first rigorous description of it. There are actually a set of waves which cross the V too. These waves are what eat up most of a ship?s energy. These wakes are long-lasting, and far reaching. There are some fantastic pictures of Kelvin wakes here.

A lot of research has gone into how to reduce this wake and the energy it drains from a ship ? one result was that you can reduce the transverse waves in the set (and the energy required to produce them) by putting a big bulbous part on the bow of the ship. But unfortunately, only at a particular speed. Here?s an interesting page on hull shapes and how they affect drag on ships.

2. The ?turbulent wake? is all the white foam kicked up by the propeller wash/cavitation and the chaotic eddy shedding at the stern. This wake tends to wash out the Kelvin waves that cross perpendicular to the direction of travel. Here?s a picture of the turbulent wake caused by an aircraft carrier. Since it?s turbulent, it tends to damp out pretty quickly.

3. The ?dead water? wake or ?narrow-V? wake, which looks like the ship flattened out the waves. This wake is also always present, but is very hard to observe, since it?s flat! Turning ships often give a good view of it, and here?s a biggie.This is a big part of what you are seeing, but this wake alone cannot last as long as several kilometers.

4. All of the above are really the surface manifestations of what is really a 3-dimensional process ? all of these wakes have a portion below the surface that is just as complex. One of the large parts of the sub-surface wake is a set of twin vortices that are shed from the stern. They are very hard to see in water, but a parallel type of phenomenon is easily observed in airplane wakes, here.

5. Now we get to the weird stuff. At certain speeds, ships can set up long solitary waves (solitons) that precede the ship. You can think of them as the ?draw-down? before the Kelvin wake comes crashing in. If you want to read some more about these, go get this PDF file.

6. The next complication is the structure of the water itself. As you probably know, very often water is stratified in layers of different temperature, salinity, turbidity, etc. This creates conditions where waves can diffract and reflect internally in these layers making all sorts of complicated effects. These can be classed as ?internal wave wakes.? In some cases, if there is a layer of material (oil, say) on the top surface, this disrupts surface tension forces that cause certain wave/wake phenomena ? these are the ?oil slicks? which are generally flatter than surrounding waters. A detailed analysis of surfactants and radar returns is here.


As you might imagine, all of these things are of great interest to people who want to know where ships are, and how to track them. Not only the military and the coast guard, but also ship traffic management and companies that are tracking their ships? progress (like express mail services that use GPS to track the whereabouts of vans, trains, etc.). Radar is very good at this, since it reflects really well from metal corners, but also very poorly from the exact features you are asking about. In radar images, what you see is a very bright ship followed by a very dark, long streak. To find out more about radar and ship tracking go here and here.

So..... the long streaks of calm water that reflect the sunlight better than the surrounding water are most probably a complicated non-linear interaction of the narrow-V, the vortices, and some internal wakes that depend on the exact structure of the water column.

I hope this helped, Lonnie!

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 Thursday, July 10, 2003

Shuttle re-entry mad science:

Asked by Steve, a Grade 10-12 student from Rushville, New York:

What is the maximum speed that a Space Shuttle will reach during Re-Entry? I'm doing a term paper on Space Shuttle Sciences. Currently I am working on the Re-Entry phase, and I need to know speeds, etc. I already know the angle of attack, and info like that - the only thing i need now is speeds. Thanks.

At first I thought this was a silly question, because it is much like asking "What is the fastest a car goes while braking?" -- and the obvious answer to that is: "Whatever speed it was going when it started to brake!" But perhaps this is a case where the person asking the question has had enough physics to know that the closer you orbit to a parent body, the faster your orbital speed. Perhaps they were thinking; ?The shuttle is coming closer to Earth, and therefore it has to accelerate to come down (??)??

So? here's the answer.

The shuttle usually operates at an orbital altitude of between 200 and 350 miles (careful! NASA often uses nautical miles for shuttle statistics), depending on what the mission and payload requirements for the flight are. A circular orbit at these heights implies an orbital speed of about 17,000 miles per hour. If the orbit is elliptical, the speed will be slightly higher, but not by much.

But how does the shuttle "de-orbit?" Basically, it has to change from flying like a spacecraft into flying like a missile, and then finally into flying like a glider. The trick is not to lose control during any of these stages, because what you do early on narrows your choices later! The first thing is to turn around so that the rear engines are facing in the direction of flight. The deorbit burn is a 2-1/2 minute firing of the Orbital Maneuvering System engines, which sit in those big bumps on either side of the shuttle's tail. Now here's the strange part -- firing backwards lowers the height of your orbit on the other side of the world! It seems totally counter-intuitive, but since you are operating in a constrained system, there are some interesting things that happen. If you want to climb higher, you wait until you are on the opposite side of the world, and fire backwards. If you want to speed up, you fire the engines facing the stars, and if you want to slow down, you fire the engines facing the Earth! No wonder those pilots need so much training!

One-half orbit after the deorbit burn is completed, the shuttle will have dropped to an altitude of 557,000 feet and be about 5,000 miles from the landing strip. At this point, it is still going about 17,000 miles per hour, but there is not enough air at this height for flying. The shuttle has to drop to 400,000 feet before it can start to use its control surfaces, still going at a speed of between 16,700 and 17,000 miles per hour (since there is nothing to brake against yet). This is still so fast that the shuttle begins to really heat up as it smashes into the air molecules faster than they can get out of the way. Between 265,000 feet and 162,000 feet altitude it is still going so fast that it actually knocks the electrons off some of the molecules, creating an ionized gas cloud that causes a 16 minute-long radio blackout. If you are lucky enough to see it go by at this stage (perhaps if you live in the Midwest, and the landing is targeted for Florida), you will see a fireball streaking throughthe sky. And I would add that this is the unfortunate point at which Columbia broke up over Texas last January -- the ionized gas probably melted the left wing structure, and there was no way out of the situation at this point. See my February 4 and February 1 blogs.

When the shuttle is about 60 miles from the runway, it starts a series of S-turns that slow it down from 1,700 mph and drop it from 83,000 feet. Finally, at about 25 miles from the runway and 49,000 feet altitude the shuttle drops below the speed of sound (this is about as high as regular jets fly). When it is about 8 miles from the runway, it is still at 10,000 feet, doing about 330 mph which is about twice as fast as a jet, and 10 times as high. The view from the cockpit at this point is pretty scary for a regular pilot ? your brain just screams at you that you are coming in WAY too steep and fast. To overcome this fear, shuttle pilots do a lot of training in specially modified airplanes that behave like the shuttle during this very last phase of landing.

I hope this helps.

Anything you ever wanted to know about the shuttle operations is at: http://science.ksc.nasa.gov/shuttle/technology/sts-newsref/stsref-toc.html

(Did you know they blow the solid rocket booster casings full with air to get them off the sea-bottom where they sink after crashing back down? Thanks ? I learned that doing research for this!)

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 Tuesday, July 08, 2003

Earth wobble mad science:

Asked by Richard, a graduate student in science, from Beardsley, MN:

How long have scientists studied the Earth's wobble? I have been told it is constant.

Whoever told you this probably meant ?the Earth is constantly wobbling,? rather than ?the Earth?s wobble is constant,? because the wobble is certainly not constant. In fact, it is chaotic, and therefore unpredictable in the long run.

We have been studying the Earth?s wobble for as long as we have been able to detect it, so it is more a question of when different observing and analytical techniques were developed, as well as technologies. As our observational and analytical capabilities increased, we discovered that there were in fact several different kinds of wobble. Like a lot of chaotic processes, the more closely we looked at it, the more detail there was!

The first level of wobble is pretty easy to understand in terms of classical physics and day-to-day experience. It is called precession--? and it is exactly the same motion as a top makes, slowly changing where its pole of rotation points because the center of mass is not directly over the top?s point of contact with the floor, and therefore gravity exerts a torque on the top. For the Earth, this motion is called precession of the equinoxes, and the torque results from the fact that the Earth is flattened at the poles and that the Earth?s axis is tilted (?inclined?) relative to the sun and so the sun is always pulling a little more on the Earth?s near-side bulge than on the far-side bulge, trying to straighten up the inclination. This is what causes the ?Pole Star? to change--?today the sky appears to rotate around a point very near the star Polaris, but precession will make other stars the ?Pole Star? in the future (and the past)! Since the cycle is about 25,800 years long, when we try to imagine the sky over ancient Stonehenge, Egypt or Sumer, precession must be taken into account, since 5,000 years ago represents almost 70 degrees around the cycle. Observationally, this change was probably detected very early on, probably by careful long-term stellar observers like the Egyptians, Babylonians and the much later Maya. Certainly we know that by the time of ancient Greece this motion was known, but not understood. If the only thing your technology was able to measure was the precession, you might think it was constant--?you would have to wait around a long time to verify the second time around!

As soon as we understood that the sun was causing torque and precession, we knew that there were other things out there torqueing the Earth around too--?the Moon certainly, but the other planets also exert tiny torques that are measurable, and these cumulatively cause the first level of detail on the cone traced out by the precession. These small deviations from the precession are called nutations, and the largest contributor is the Moon?s pull on the Earth?s bulges, causing an oscillation with a period of about 18.6 years.

As soon as we figured out dynamics and moments of inertia etc. we were able to predict other types of wobbles. When you spin an object around an axis that is not one of its principal axes, it will wobble (sometimes pretty violently; try spinning a rubber-band bound book around on various axes to see what happens). Euler applied this theory to Earth, and in 1758 predicted that an extra level of detail in the wobble should be observable with a 304 day period since the Earth was not quite spinning around its flattest point, but this wobble was not detected until 1891 by Chandler (who found it was in fact 435 days long). Euler?s calculation was for a perfectly rigid body with the shape of the Earth, but since the Earth is not quite rigid, the longer period is observed. This wobble is now called the ?Chandler Wobble? and is observed to be truly chaotic, sometimes collapsing to be almost unobservable, and sometimes growing to change the location of the pole of rotation by about 10 meters (see the USNO explanation of Earth orientation). We still do not fully understand what causes these changes, but it is definitely an internal process, probably something like damping in the fluid outer core, or mass redistribution in the mantle. We do know that since the mantle and the core have slightly different shapes they will nutate at different rates, so there is constant friction at the core-mantle boundary due to this differential nutation. Chandler was an observer and calculator of the first order, despite having only a high school degree (for more on him see his biography).

The finest level of detail observed so far are the changes in the length-of-day (LOD). Each day differs in length from others at a level of several milliseconds, and so this has only been recently observed, although it was predicted by Kant in the 1750s. The pattern of these changes is partly regular, and partly chaotic. We see regular annual variations and a variation with a period of about 200 years, and several chaotic ?patterns? with typical scales of several years to a few days. Just as that ever-spinning skater spins faster or slower depending on how she holds her arms and leg, the Earth will spin faster or slower depending on where there is more snow, water, air, rock, etc. Some of these things move around easily, some do not. Again, these individual causes can be understood easily in terms of classical physics, but there are so many possibilities that actually identifying which change causes what difference in the length of day is impossible. Since the root cause of LOD variations is the redistribution of mass in the Earth system, this must also affect the Chandler Wobble, but these changes are so slight we have not detected them yet.

To complicate all this a little more (you knew that was coming, didn?t you?), there are some other changes in how the Earth moves. The inclination of the Earth?s axis actually varies between about 21.5 degrees and 24.5 degrees with a period of about 41,000 years (present value is 23.5 degrees). This obviously affects precession and nutation. There is also a change in how elliptical the Earth?s orbit is around the sun, varying from 0.01 to 0.007, with a period of about 92,400 years--?this change affects precession rates very markedly (present value 0.016). So we have a lot of wobbles going on at the same time, some of them directly coupled to each other, some indirectly. With periods ranging from several days to almost 100,000 years, you can imagine that there is plenty of opportunity for some rather complex interference between the various phenomena. This produces the chaotic behavior that we observe, and which we believe is typical for multi-planet solar systems.

For a good discussion of these concepts at an advanced high-school level and how they affect climate, see The Motion of the Earth in Space.

I got some of the historical part of this from Historical Development of Earth Rotation Knowledge.

 Monday, July 07, 2003

Minor planet mad science:

Asked by Sam, a student in grades 10-12:

In which constellation could you find the minor planet 719 Albert?

Well, since Albert is really zipping along, it depends when you look. This summer it will actually be in a pretty good position for observers in the Northern hemisphere ? but even though it will pass pretty close to Earth, it?s pretty small (between 3 and 6 km radius) so it will be very dim and only observable through a large telescope.

Today, June 13 2001, Albert is in Delphinus, but by tomorrow it will have moved into Equuleus. Albert moves on into Pegasus by June 18, where on July 31 it will reach its highest point in the sky. Albert will move into Andromeda by August 8, where it then starts to go into retrograde motion as the Earth overtakes it (where it looks like it?s moving backwards, like a car you are overtaking, even though both of you are still moving forwards). By August 18 it will cross into Pisces, and by September 1 it is in Aries, where on the 5th it will reach its closest approach to Earth, about 43 million kilometers.

OK. Tell me more. Albert has an interesting history. The number (719) refers to the fact that it was number 719 in a list of asteroids that astronomers started making over two hundred years ago. It was discovered in 1911 by an Austrian, Johann Palisa, who was working in Vienna, and it was also seen by a Danish observer within a few days after. But then they lost it!

How can you lose an asteroid? Aren?t these things big? Umm, well, yes, but space is even bigger, and there?s a lot of it out there. Even something as big as 6 km across looks pretty small when it is several tens of million of kilometers away! Also, we need to observe objects several times (and be sure we are actually seeing the same one) to be able to figure out their orbit ? and the two times Albert was seen in 1911 were not enough to give us a good estimate of the real orbit. In fact, the next time we looked for it, we were off by several degrees, which, when you look though a big telescope, is a HUGE error.

So, how did we find it again? An astronomer in Arizona called Jeffrey Larsen observed an object on May 1, 2000 that he called 2000 JW8, which was tracked by Larsen and several others for several days to better determine its orbit. By May 9, Gareth Williams of the Minor Planet Center was able to determine that 2000 JW8 was in fact the long-lost Albert. (You can run the 2000 JW8 orbit ?backwards? and tell that it was in the right place in 1911).

So how do you know where it is now? To tell where any orbiting object is, you need seven pieces of information. The best way to think of it is as follows: you need three to tell you where it is (x, y, z) and three more to tell you how fast it is moving (Vx, Vy, Vz), and one more to tell you what time it was when you took these measurements (t). In real life, measuring orbits using x, y and z is REALLY HARD, so astronomers use another set of seven measurements that sound really strange (see below), but they are essentially giving us the same information. Then you use the laws of physics to tell you how the object will move either in the future or the past. It turns out that Albert orbits between the Earth and Jupiter, and will come ?close? to both planets on this time round the Sun. Albert takes about 4.28 years to orbit once, and comes close to Earth almost exactly every 30 years (...1911, 1941, 1971, 2001...).

I?m game ? gimme the full set of numbers in all their gory detail OK, here goes. These are also called the ?Orbital Elements.? You can use these in a lot of astronomy software for computers to see pretty much where Albert will be anytime. That?s how I figured out where it was over this summer ? I just plugged these elements into a pretty simple program on my Mac and presto!

Semi-major axis (a): 2.636667 a.u.
Eccentricity (e): 0.548273
Inclination (i):11.3095
Longitude of Ascending Node: 184.9305 (Epoch 2000.0)
Longitude of Perihelion:154.2885
Epoch (T): 2001 August 21.2582
Mean Motion (n): 0.2302084


Here are two good articles on 719 Albert that cover its history and rediscovery:
http://cfa-www.harvard.edu/cfa/ps/pressinfo/Albert.html
http://neo.jpl.nasa.gov/news/news102.html

And here is the technical bulletin that gives the gory details:
http://cfa-www.harvard.edu/iauc/07400/07420.html

An interesting website is the Spacewatch project of the Lunar and Planetary Observatory of the University of Arizona, who watch for asteroids all the way out to the orbit of Neptune:
http://www.lpl.arizona.edu/spacewatch/

 Tuesday, July 01, 2003

Apollo LM mad science:

Asked by a non-science university graduate:

What happened to the Apollo LEMs after docking with the CSMs? (I Suppose the crashed back onto the Moon's surface. At what velocity did they crash?)

Yes, they crashed back on to the Moon, and it was done on purpose, to provide noise for the seismometers to be able to get data on the Moon's deep interior.

You got me curious, so I went and found out what happened to all the Lunar Modules.

Grumman Aerospace built 16 LMs of human-flight-ratable quality, and several additional modules (also known as "lunar test articles," or LTAs) that were used for unmanned flights and ground testing (including test-to-failure).

By the way, the early name for this spacecraft was Lunar Excursion Module (LEM), but NASA felt that the word "Excursion" gave it a frivolous feel, so they got rid of it, and the official name for the spacecraft became Lunar Module (LM) -- but by that point the pronunciation was fixed, and LM was pronounced "lem" and that has confused everybody ever since (including you and me!). (Reference: http://www.hq.nasa.gov/office/pao/History/SP-4205/ch14-6.html).

I'm sure you know, but for completeness I should state that the LM was actually composed of two stages; the descent stage, which carried the motor that slowed the LM on its landing (basically the lower part with the legs), and the ascent stage which was the strange looking upper part in which the astronauts actually stayed, and which carried them back to the CSM in lunar orbit. Your question refers specifically to the fate of the ascent stages of the LMs except in the cases of Apollo 10 and 13 (see below).

In chronological order of LTA and LM flights (or scheduled flights), this is what I found for you:

1. Apollo 4 - launched 9 November 1967. The first all-up launch of Saturn V rocket (unmanned) carried LTA-10R into orbit, which was completely destroyed on re-entry into the Earth's atmosphere.

2. Apollo 5 - launched 22 January 1968. First test of LM1 in space (unmanned). This LM had no legs. The LM's orbit later decayed and LM1 re-entered atmosphere several hundred kilometers SW of Guam on February 12 1968. (http://www.hq.nasa.gov/office/pao/History/SP-4205/ch10-3.html)

3. Apollo 6 - launched 4 April 1968. LTA-2R carried into orbit, and was destroyed on re-entry into the atmosphere. This flight was to have carried LM2, but due to the success of Apollo 5 LM testing, LM2 was never flown, and LM2 now sits in the National Air and Space Museum in Washington DC.

Apollo 7 and Apollo 8 did not carry LMs, despite having LM Pilots along in their crews.

4. Apollo 9 - launched March 3, 1969. Extensive manned flight-testing of LM3 "Spider" in Earth orbit, carrying out in-space engine tests and maneuvers equivalent to those that would be needed for lunar orbit rendezvous. LM3 becomes the first non-re-entry capable spacecraft to carry humans (i.e. if something went wrong with the CSM, there was no way home). The LM was jettisoned into a highly elliptical orbit (237 km perigee, 6900+ km apogee) that later decayed. LM destroyed on re-entry into atmosphere.

OK, now I finally get to answering your exact question...

5. Apollo 10 - launched May 18 1969. LM4 "Snoopy" goes to the Moon, and descends to within 14,447 meters altitude of the lunar surface, where the descent stage was jettisoned. The descent stage simply fell to the surface, so it impacted at approximately lunar free-fall from this height, 152 m/s or 547 km/hr. The ascent module, on the other hand, was jettisoned after re-docking with the CSM in lunar orbit, and then its engines were fired, injecting it into a solar orbit where it still exists! People often ask if this crew was tempted to land, but it should be pointed out that the ascent module was incapable of climbing back all the way from the surface (insufficient fuel), so the crew knew it would have been stranded had they actually landed.

6. Apollo 11 - launched July 16 1969 LM5 "Eagle" left the descent stage on the Sea of Tranquillity, and the ascent stage was jettisoned 2 hours after docking with the CSM. This orbit decayed, and it crashed onto Moon, but we are unsure where. This impact velocity was much much greater, not only because it was in free-fall from a much higher altitude (the CSM orbited at about 111 km above the surface), but because the forward velocity was at least 600 km/hr as well. My estimate for a minimum speed at impact is 1,600 km/hr. The seismometers left on the Moon by the crew registered the impact of the ascent module. (But note also that all the Saturn IV-B translunar injection stages also crashed onto the Moon before their respective LM's arrival -- this velocity had to be staggering, since the stage was basically accelerating all the way from the Lagrange point inwards!)

http://www.hq.nasa.gov/office/pao/History/SP-4205/ch14-6.html for mission details

http://nssdc.gsfc.nasa.gov/planetary/lunar/images/a11lmreturn.jpg for a photo of Eagle after being jettisoned.

http://www.hq.nasa.gov/office/pao/History/ap15fj/loressay.htm for a GREAT page on the physics of getting the LM to get back to the CSM, which was actually more difficult than getting to the Moon itself!

7. Apollo 12 - launched November 14, 1969 LM6 "Intrepid" also left the descent stage on the Moon, on the Sea of Storms. The ascent stage was jettisoned and crashed at the lunar coordinates 3.94 S, 21.21 W, probably at a very similar velocity to LM5.

8. Apollo 13 - launched April 11, 1970 LM7 "Aquarius" was the famous lifeboat that saved Lovell, Swigert and Haise after an explosion on the SM. The LM descent stage was used to insert the LM-CSM into a trans-Earth injection orbit, a task for which it was never designed. LM7 burned up in Earth's atmosphere after it was jettisoned just prior to CM re-entry procedures began.

For great info on the orbit used by the Apollo program, go to http://www.christa.org/lunar.htm, and especially the diagram at http://www.christa.org/lor.htm which shows the various orbits very clearly.

9. Apollo 14 - launched January 31, 1971. LM8 "Antares" also left the descent stage on the Moon, on the Fra Mauro highlands. The ascent stage was jettisoned and crashed at the lunar coordinates 3.42 S, 19.67 W, probably at a very similar velocity to LM5.

10. LM9 was originally scheduled to fly on Apollo 15, but the J-series redesign of the LM to include the rover and extended stay capability made it obsolete. It now sits at the Kennedy Space Center Visitor's Center.

11. Apollo 15 - launched July 26 1971. LM10 "Falcon" was the first of the J-series, heavier LMs. The descent stage was also left on the Moon, in the Hadley Rille area of the Apennines. The ascent stage was jettisoned and crashed at the lunar coordinates 26.36 N, 0.25 E, probably at a very similar velocity to LM5, despite a much higher orbital inclination.

12. Apollo 16 - launched April 16 1972. LM11 "Orion" - descent stage was also left on the Moon, in the Descartes highlands. The ascent stage began to tumble immediately after being jettisoned, so the lunar impact site is unknown.

13. Apollo 17 - launched December 7 1972. LM12 "Challenger" was the final LM to reach the Moon. . The descent stage was also left on the Moon, in the Taurus-Littrow area of the Sea of Serenity. The ascent stage was jettisoned and crashed at the lunar coordinates 19.96 N, 30.50 E, probably at a very similar velocity to LM5

14. Apollo 18 - this mission to Copernicus Crater was cancelled in September of 1970, so LM13 was not used. It now belongs to the Cradle of Aviation Museum on Long Island, and was used by HBO for filming "From the Earth to the Moon"

15. Apollo 19 was also cancelled in September of 1970, so LM 14 was not used. It now belongs to the Franklin Institute in Philadelphia.

16. Apollo 20 was cancelled earlier, on January 4, 1970, along with the manned mission to Mars. LM15 was scrapped by Grumman before making it off the assembly line.

A final module, MSC-16, now sits at the Museum of Science and Industry in Chicago, IL. -- this is a LTA, and served only as a training vehicle.

If you want to find out where many components of the American program are now housed, a great resource is the following page: http://aesp.nasa.okstate.edu/fieldguide/frames.html -- you will probably find some piece of American space history is housed nearby.

James McDivitt (Commander, Apollo 9) to Grumman Aerospace workers: "Thanks for the funny-looking spacecraft - It sure flies better than it looks!"

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Thurmond, Hepburn:

I have to admit that I was more affected by the news of Katherine Hepburn's passing than that of Strom Thurmond. But that's a sign of how much exposure I had to them -- I saw Hepburn a lot more than Thurmond because of her movies. What if Strom had acted in "African Queen" -- would I remember him as fondly? How about Strom Thurmond in "Guess Who's Coming to Dinner?" Hmm. And as a male, I have to say that she was definitely more attractive than the late honored Senator.

What is it about high cheekbones? Is it simply a fashion of the times that defines what beauty is, or is it truly engraved in our DNA, and what we perceive as a good match? And how is intellect interfering with all of this?

There are some great studies out there in cognitive science that look at how we perceive different faces, and although a lot of it seems like it is to do with how we perceive different expressions, I think the tools are there to do some interesting research on perceptions of attractiveness. Is it based on where you were brought up? Is it based on exposure to media? Is it based on race, culture, and/or ethnicity? How similar are the features on finds attractive to one's parents? etc. etc.

Off to write a grant... oh damn it, I can't. I work for the people that fund the grants. Sheesh.

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